The human operator's manual control behaviour under time-invariant conditions has been successfully modelled. However, significant gaps remain in understanding and modelling adaptive manual control behaviour under time-varying conditions. One such less-understood aspect is the pilot's ability to detect changes in time-varying controlled element dynamics. This study aims to develop a mathematical model that investigates open-loop stability as a criterion in compensatory and pursuit tracking tasks to model the pilot's detection of change in controlled element dynamics across different transition rates, particularly for transitions from stable to less-stable vehicle dynamics. The model operates under the assumption that trained human operators track statistical properties of tracking task signals within periods of compromised open-loop stability to trigger their detection of change in dynamics. The model identifies regions of reduced stability and simulates the tracking task signals through time-varying computer simulations. Subsequently, human-in-the-loop experiments are conducted to validate the model. The validated model demonstrates a combined accuracy of $88.54\%$ for the compensatory task and $80.62\%$ for the pursuit task. Notably, in the experiments, the error signal consistently outperforms the error rate signal across all transition rates, diverging from the results of the computer simulations. Overall, the proposed model's ability to successfully predict pilot detection across a spectrum of transition rates marks an advancement towards developing more human-like automation.